It depends on who you are and what you are accustomed to. As a general rule Park Slope is the place to go. It is a section of Brooklyn just north of Prospect Park. The good places are anywhere the streets are numbered 1-10 and the avenues are numbered 1-8.
BTW Park Slope is one of the most expensive sections in Brooklyn. You will likely pay about $1000 for a reasonable place there.
I moved to East Flatbush (about 5 blocks from the school). I'm used to the neighborhood, so I am able to take advantage of the "relatively" low rents there (if you consider $1200 low rent).
You may also want to consider Clinton Hills and Midwood. Both are along Flatbush avenue, and are a little more reasonable price-wise than Park Slope. They are all pretty convenient to Downstate by bus or train.
[This message has been edited by Sheon (edited 07-07-2000).]